Full page version of the visualizer here.
Tried to explain basic concepts in nuclear reactors using plain language and visualizations. Got carried away with the idea of a javascript particle monte carlo code. It is a bit garbage, but the visualization is nice and the results are not completely off despite some radical simplifications.
Took a little longer than expected. Don't recommend web dev work.
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SpaceX’s Falcon 9 is like a Toyota Corolla – an order of magnitude cheaper than competitor’s “high performance” rocket systems, the Ferraris, but achieving the same basic transport requirements with greater reliability and safety. Before Falcon, space launch was a Ferrari-like industry, with handmade, highly specialized, extremely expensive vehicles targeting government customers and fully complicit in the inefficiencies of government contracting. Similarly, the nuclear industry produces and still designs Ferrari-like fission reactors, with high performance metrics in terms of power density and unit power, at a megaproject scale, but with high system and operational complexity, extreme development cost, numerous part counts, and very low production and deployment rates that still require human-machine interface to meet societal safety objectives. The demand for nuclear Ferraris in the U.S., particularly within non-traditional energy utilities is very low, as few competent utilities want unique reactors with such high capital costs, running at such high power that low probability accidents can have offsite consequences. Where is the nuclear Corolla?
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The general public and even most nuclear engineers do not understand how easy it is for nuclear fuel to fail. Since the dawn of the nuclear era, nuclear fuels have been designed and built to meet only a small portion of the full requirements. This was due to material and technology limitations as well as costs. The only economical and practical way to use nuclear material for power has been simple fuel oxide pellets in metal cans.
That is now changing with the introduction of TRISO particle based fuels and use of advanced radiation tolerant ceramics. In this post, I will explain the performance goals of nuclear fuel and then show how normal fuels compare relative to TRISO based fuels.
Still there's a limit to what I can do with words. I can write all about nuclear accidents and the performance characteristics of traditional fuel compared to new TRISO-based fuels, but people often don't get it. The technical discussion of materials in nuclear reactors and how they affect fuel performance is not straightforward. But the practical differences between traditional and TRISO-based fuels would be plainly obvious if we could observe the fuel forms in action. We can't visually observe nuclear accidents as cameras can't survive the radiation, but we can show what happens using animations. So I rigged up a quick animation showing how traditional fuel and TRISO/FCM fuel look like as they encounter the same or similar conditions. I've made simplifications for the sake of comparison and illustration, but the general idea stands that during severe accidents, traditional fuel will fail to the point of melting and vaporization while TRISO/FCM fuel remains solid and functional.
As a side-project, I collect and maintain information on upcoming nuclear energy extraction systems. Having it all in one place makes it useful for the public at large, policymakers, and scientists looking for a better understanding of the unfolding nuclear technology landscape.
There are now many designs, perhaps as many as 100 that are actively developed with more than a handful of people. To an outsider, these designs are all the same or arbitrarily different. Neither perception is true - there are important differences concerning cost and safety that should be more widely discussed.
We should build a nuclear powered monument that could last several thousand years. A reminder to future generations, human or not, that we existed and we thought of them. And I want it out in the open – not like that silly 1000-year clock buried in a hole in the middle of nowhere in Texas. More like the Pyramids or the great churches from our past. What should it be and how will it be powered?
This is a TRISO particle from Ultra Safe Nuclear. The central sphere is a nuclear fuel like Uranium Carbon Oxide (UCO), and the shells are made of various ceramics.
2024/10/16 Note: since I wrote this in 2022, Google and Amazon have decided to invest in the technology and development of pebble bed TRISO-fueled with Kairos Power and X-Energy. They must have forgotten to click the subscribe button on my newsletter! I predict both these projects will be completed but neither will be pursued for larger gigawatt scale rollouts without dramatic design changes approaching prismatic HTGR.
High temperature gas-cooled reactors (HTGR) come in basically two flavors: prismatic cores and pebble-bed cores. Both use graphite moderator and TRISO fuel particles to make the core which allows the reactor to reach high temperatures and handle accidents with relative ease. Both use helium to cool it, which allows thermal applications up to 950°C and power conversion efficiencies of 40%-55%, compared to just 300°C and 30% in water-cooled reactors. They differ in the geometry and form factor of the moderator and fuel which leads to significant differences in size, operations, and technology roadmaps.
In prismatic cores like the Ultra Safe MMR or Japan's HTTR, graphite is formed into chair sized hexagonal blocks with holes for cylindrical fuel pellets and separate holes for coolant channels. The core is maximally packed and nothing moves. Refueling the reactor involves swapping out the graphite blocks.
In Pebble Beds like China's HTR-PM or the very similar X-Energy Xe-100 design, the fuel and graphite are packaged as balls (called pebbles) that are poured into the reactor from the top and emptied at the bottom in a continuous fashion like a gumball machine. The basic working principle of a pebble-bed is shown below.
This post is primarily about pebble-beds but provides the needed comparison to prismatic HTGRs to illustrate the benefits or drawbacks. For the most part, I focus on the drawbacks that are unique to pebble-beds as most of the benefits apply to both prismatic and pebbled-bed reactors.
The conventional UO2/Zircaloy fuel and TRISO based fuels are introduced below on the basis of how they address or exacerbate the hazards present in a nuclear reactor. Compared to conventional fuel, TRISO aims to contain and limit the fission product risk at a much smaller scale with higher performance materials thereby limiting the state space and growth of periphery coping systems. TRISO’s hazard reduction goes far beyond that of conventional fuel. Its potential to allow for simplified reactor systems may outweigh its higher fabrication costs.
Conventional nuclear fuel is UO2 oxide pellets inside a Zircaloy tube, called a cladding. As the fuel is used, the UO2 expands and crumbles into pieces and pressurizes the Zircalloy tube. The fission products, gases, and solids, are released into the tube, creating a high pressure (>40MPa) in the tube. Just beyond the coolant operating conditions of roughly 400 °C, the Zircaloy tube will experience excessive corrosion over its 4-6 year lifetime. By 700-900 °C Zircaloy tube can burst and by 1000 °C it can generate significant amount of hydrogen gas in an exothermic reaction with water. In any of these cases, if the UO2 fuel operates at greater than 800 °C, fission gases are released into the coolant. The hydrogen generation from Zircaloy, if left unmitigated and its underlying critical safety functions for a reactor will likely lead to a hydrogen explosion or fire. The containment will then hold the pressure of the accident and withstand impacts of hydrogen explosions, fires, and elevated temperatures. If helium is utilized as the coolant, then the limiting temperature for conventional fuel is closer to 800 °C. Even at 1000 °C, very limited fission gas inventory is released from UO2 pellets.
Originally conceived in 1957 1 during the British Dragon program, TRistructural ISOtropic (TRISO) particle fuel consists of fissile Uranium or Thorium fuel kernels measuring 250 to 600 μm across and coated with layers of Pyrolytic Carbon and Silicon Carbide (sometimes ZrC for NTP applications). TRISO particles are the fuel spheres with ceramic layers, while the matrix is the ceramic material that surroundings the TRISO particles to form a consolidated fuel pellet, usually a cylinder, measuring about 1-2 cm in diameter. The matrix is traditionally graphite, but use of SiC has also been explored.
The driving idea behind TRISO particle fuel is to give each 250 to 600 μm sized piece of nuclear fuel its own containment and pressure vessel to enhance the fuel’s ability to contain fission products at very high temperatures and neutron bombardment. The physical basis for miniaturizing the pressure vessel is twofold: fuel subdivision and pressure vessel enhancement.
First, subdividing the nuclear fuel by four to five orders of magnitude significantly reduces the risk of single point failures in the pressure vessel or fuel cladding. Ordinarily, if a single failure in the reactor’s main steel pressure vessel or one or few fuel cladding is significant enough, it can lead to a radioactivity release that requires plant shutdown and costly cleanup. With TRISO, particles fail at rates of 10^-5 during operating conditions, and when they occur, lead to a small radiation release into the fuel matrix where it can be stopped to a degree. With TRISO, fission product retention is achieved at the millimeter scale and by high performance ceramics which limits the accessible state space and the growth of periphery systems at a larger scale. Addressing problems at the smallest feasible scale reduces the required overhead containment effort before they have a chance to grow in size, area, and rate. In fact, U.S. NRC has accepted he idea of a “functional” containment and for HTGRs, it is expected to not require expensive pressure retaining containments. With conventional fuel, much effort must be taken to prevent their escape. Subdivision of fuel into particles is even believed to provide blast resistance as the particle may be small and durable enough to remain intact during explosive fractures like a direct missile hit. Indeed, with this reasoning in mind, the US Department of Defense began funding development of TRISO fueled reactors for forward bases in early 2019.2
The second advantage to miniaturizing the pressure vessel is the ability to enhance pressure vessel performance through use of thin layered ceramics in a mass manufactured, seamless, spherical design. Fabrication of millions of particle pressure vessels can be highly standardized and controlled in a mass manufacturing environment with defect rates of 1 in 100,000.3 Crucially, the millimeter scale vessel allows the use of highly pure brittle ceramics made through CVD techniques that maintain high strength and stability under high temperature and irradiation and have dual use as low reactivity fission product barriers. Normal reactor pressure vessels are made one at a time and have to be cylindrical, with various seaming and joining techniques, multi cm wall thickness, and cannot use brittle materials. As the pressure vessel size is reduced, the more efficient spherical geometry can be adopted, and the required wall thickness drops dramatically to the point that a 35 μm SiC layer can indefinitely contain gas pressures in excess of 200 MPa.4 This compares to the main reactor steel pressure vessel which may go as high as 15MPa or the Zircalloy cladding which can have pressures up to 50-100 MPa in high temperature conditions. As the nuclear fuel fissions, it continues to accumulate fission product gases and increases the gas pressure that must be contained. If the pressure vessel can handle higher pressures, the fuel can be burned more extensively and safely, which means more efficient use of fuel.
The attractiveness of TRISO-matrix fuel is derived from its ceramics' high thermal conductivity, high fission product retention, and superior irradiation and corrosion resistance across operating, accident, and storage conditions. This translates into better efficiency and safety for current civilian reactors (operation at higher temperatures with higher safety margins) as well as upcoming micro reactors, gas cooled reactors, and molten salt cooled reactors. More extreme performance applications enabled by TRISO-matrix type concepts include nuclear thermal propulsion (NTP) for space, VHTR, Subterrene tunneling, and nuclear ramjets.
TRISO is traditionally packaged into graphite pellets. These pellets are formed through a high pressure and high temperature process with various organic binders. The process allows for only simple pellet shapes and can lead to overstressing of the particles, though this can be controlled. Although the TRISO particle is an excellent fission product retention device, some fission products like Ag and Ce can leak into the coolant. More particles will fail as temperatures are elevated in the core during extreme accident conditions. The graphite pellets or pebbles will tend to undergo irradiation induced swelling and property changes and sometimes crack, impacting the heat transfer from fuel to coolant and complicating spent fuel handling with extra processing steps before permanent storage.
TRISO particles must be packaged into a fuel form or pellet, and SiC encapsulation, also known as Fully Ceramic Micro-encapsulated Fuel (FCM)5 or Fuel-in-Fiber 6, offers a series of benefits over graphite including higher fission product retention, greater tolerance to air/steam ingress, and potentially higher burnup capability. The most significant benefit to SiC encapsulation is that the additive process used in its manufacture can achieve around 65% packing fraction with little to no stress on the TRISO particles during manufacturing, although this can ostensibly be accomplished with graphite as well. This process also gives design freedoms for near-arbitrary fuel form factors such as annular fuel and other highly specified shapes that can vary 3-dimensionally across the core.7 This allows a reactor to operate at higher power and with greater energy content without increasing temperatures in the fuel. Other benefits include reduced dimensional changes of the pellets, reduced thermal property changes of the pellets over time and radiation damage. SiC ends up swelling instead of shrinking and its swelling saturates after 1 DPA.8 Finally, the SiC or graphite encapsulation creates a ready-for-storage form factor that is simpler to handle than traditional crumbling fuel pellets and a step above simple graphite encapsulated TRISO.
SiC-encapsulation may enhance the resilience of TRISO particles to higher temperatures and irradiations allowing for more extensive burnups, higher power densities, and extreme accident tolerance. Higher burnups allow for a reduction in the long-lived fission products, reducing the spent fuel’s radioactivity lifetime to thousands of years rather than hundreds of thousands.
HALEU greater than 5% enrichment does not exist in the US outside the military complex, and significant quantities are unlikely to be available for demonstrations before 2030, let alone commercial rollouts. The capability to use lower enrichment fuel unlocks several benefits with a cascade of knock-on advantages. The lower enrichment fuel improves the risk profile for technology demonstration and deployment. Supply chains do not have to be created from scratch and favorable regulations and facility requirements are allowed for lower enrichment fuel, which will directly impact fuel fabrication and reactor manufacturing costs. Finally, lower fuel enrichment reduces strategic value and proliferation risk because it takes more effort to further enrich to weapons capable grades.9
K. Verfondern, H. Nabielek, and J. M. Kendall, “Coated Particle Fuel for HTGCR.” ↩
“PELE PROGRAM PHASE I.” ↩
Petti et al., Triso-Coated Particle Fuel Performance. ↩
Hales et al., “Multidimensional Multiphysics Simulation of TRISO Particle Fuel.” ↩
Snead et al., “Fully Ceramic Microencapsulated Fuels: A Transformational Technology for Present and next Generation Reactors-Properties and Fabrication of FCM Fuel.” ↩
Hiscox and Shirvan, “Reactor Physics Analysis of a New Accident Tolerant Fuel Called Fuel-in-Fibers.” ↩
Terrani et al., “Architecture and Properties of TCR Fuel Form.” ↩
Snead et al., “Handbook of SiC Properties for Fuel Performance Modeling.” ↩
Glaser, “About the Enrichment Limit for Research Reactor Conversion: Why 20%?” ↩
A nuclear reactor contains many hazards that can ultimately lead to a Fission Product (FP) release including decay heat, excess reactivity, chemical reactions, and high pressure. Hazards can be considered the potential gradients that can or could become accessible and who equilibration can lead to fission product release.
The fission products in the fuel are the underlying hazard. Fission product gases are concentrated in the fuel at high pressure and temperature, but nonexistent in the low temperature and low-pressure environment. This form a chemical difference that would like to equilibrate to the disadvantage of lifeforms outside.
Each hazard is listed in the table below with the mitigating approach taken in the HTGR architecture. Each in their own, the hazards can be mitigated through passive mechanisms and inherent characteristics. The International Atomic Energy Agency’s (IAEA) definition of inherent safety being “safety achieved by the elimination of a specified hazard by means of the choice of material and design concept” and their logic on the various categories of passive systems is followed.1 The second Table discusses various design choices, and their effects on the hazards.
| HAZARD | Description |
|---|---|
| Chemical Hazard | Core components can interact with each other, the coolant, or external water and air to release energy or cause corrosion. At a minimum, this exacerbates maintenance and inspection needs during normal operations. During accidents, these features escalate conditions beyond the point of no return such as when Zirconium and water react at elevated temperatures to release energy and hydrogen which can then explode resulting in loss of control functions or LOCA. Similar problems occur with sodium coolant and heat pipes. |
| Reactivity Hazard | Control rod extraction or other mechanisms can cause the reactor to become dangerously supercritical and dramatically increase the power output of the reactor beyond what it is capable of handling. Too much power and the fuel will melt itself, releasing fission products. Most reactors can somewhat tolerate the partial ejection of one or two control rods but will fail catastrophically when more are extracted. |
| Terrorist Hazard | Bad actors may intentionally sabotage reactor components by explosive or kinetic means. Bad actors could intentionally withdraw all reactor control rods, cause intentional coolant depressurization or flooding. |
| Pressure Hazard | High pressure constitutes a stored potential energy that can be released explosively leading to impacts and damage to reactor components or the release of radioactive coolant. Pressure can escalate accidents. |
| Decay Heat Hazard | When a reactor shuts down, it continues to produce some fraction of the power as decay heat for hours and days. This decay heat is what leads to reactor melting, when the reactor operators are unable to cool the reactor down, such as in the case of pipe clogging, loss of power for pumps, or loss of coolant. |
According to several studies, a TRISO fueled HTGR reactor is the highest TRL Generation IV technology 2, the most able to mitigate chemical and reactivity insertion hazards, and has sufficient acceptance from regulators and nuclear skeptics 3. This perspective is becoming mainstream in academic 4 and industrial circles with HTGR being the most heavily invested advanced reactor technology besides LWR SMRs. It is postulated that this class of reactors can be characterized by small unit power systems connected to a large balance of plant, with few or no safety systems or safety grade equipment and lower operating costs. For HTGRs, this risk reduction is principally achieved by limiting power rating and using refractory ceramic materials so that fuel temperatures do not exceed limiting temperatures during simultaneous Beyond Design Basis Accidents (BDBA), assuming an appropriate degree of security and safeguards is provided to the reactor, and all while using only Class A Passive safety mechanisms. This reactor technology is called the Class A HTGR (CA-HTGR), which more or less mirrors the design architecture of the commercially developed USNC MMR.
| Hazard | HTGR Approach |
|---|---|
| Chemical Hazard |
|
| Reactivity Hazard |
|
| Terrorist Hazard |
|
| Pressure Hazard |
|
| Decay Heat Hazard |
|
In the biological realm, there are various empirical relations associating an organism’s dimensional parameters and other characteristics. The general form is shown below. For example, if bone strength is limited in biological structures, we would expect the cross-sectional area of bones to scale with the mass or volume to the 2/3rd power. Other relations include heart rate and cruising flight speed , each with their own underlying physical explanations.
Kleiber’s law [^1] [^2]relates the mass or volume of an organism with its power rating. Figure 14 shows how organism power rating is constrained in a fashion consistent with a maximum surface heat flux boundary condition. Organisms must dissipate heat and remain at safe temperatures, and they are constrained by their surface area and the temperature limits of Earth-based biological processes. The power law varies somewhat between insects, mammals, birds, and trees, but the overall trend in the figure below has between .6 and .85, meaning that specific power decreases with mass. This is slightly better than a constant heat flux boundary condition. This basically means organisms can only give off so much energy per unit area without overheating. Solving for the maximum heat flux for spherical plants and animals yields 22 and 83 W/m2, and HTC between 1-20 W/m2K. The greater cooling capabilities of animals and birds could be due to evaporative cooling, internal liquid cooling, higher flow rates, and higher thermal conductivity.
Another way to think about Kleiber's law is in terms of power density. Considering the mass is proportional to the volume, we can recompute Kleiber's law for power density by dividing the y-axis by the x-axis. Smaller organisms have higher power density.
Kleiber's law indicates that mice have much higher power density than elephants. This is significant, because power density is a key driver of performance and cost.
Why might evolved structures have developed this relation between power and volume? We can speculate that it is the most survivable and successful way to design a power system because it more or less retires the risk of overheating.
The existence of Kleiber’s Law in evolved systems inspires its application to man-made thermal power systems that aim for passive safety and reduced risk through reduced consequence. How might these heat flux boundary conditions apply to mechanical systems like nuclear reactors? The temperature limits of typical biological processes are about 40 °C – much lower than metal and ceramic based systems. The bodily flows homogenize temperature across the body so that the maximum temperature gradients are at most a few degrees. Low surface heat flux is likely due to low temperature difference between the outer wall and the ambient. A mechanical system using metals and ceramics will be able to achieve far higher centerline temperatures and wall temperatures and a larger heat flux boundary condition.
A nuclear reactor can operate at whatever desired power rating you want. You just have to be able to extract the heat fast enough and also make sure you can do so during accident conditions. How have we picked the power rating for our nuclear reactors? We were inspired by Kleiber’s law to constrain the power according to the size, ensuring we can maintain low temperatures during accident conditions using only passive cooling mechanisms. The result is the Micro Modular Reactor, which is, in some ways, a bio-inspired nuclear reactor.
[1] Banavar et al., “Form, Function, and Evolution of Living Organisms.”
[2] Ballesteros et al., “On the Thermodynamic Origin of Metabolic Scaling.”
I'm not sure, but I think it's possible that my work at USNC heavily popularized the concept of power density and surface area to power ratio (SAPR) as metrics for reactor safety. It's a great and simplying metric that allows for a quick comparison of reactor safety amongst many different designs. And of course it was the fundamental innovation that led to the development of the MMR: unlock robust passive safety by maximizing the surface area to power ratio and minimizing the power density.
A nuclear reactor can be operated at any desired power provided that the heat can be carried out of the core. In practice, the power is limited by industrial ability to make and deliver large components and the limiting temperatures of the fuel and materials in a given cooling architecture during operating and accident conditions. If cooling does not match the heat generation, temperatures increase, and the reactor will essentially turn off beyond certain temperatures. It will similarly shut down if it melts into a non-critical configuration – but the battle is lost with large remediation costs and leakage concerns even with a functional containment.
Traditionally, reactor power density has been determined by the maximum heat transfer that can be achieved with the given geometry and cooling fluid during operating conditions and favorably defined accident conditions. And power rating is determined by simply applying the power density to the entire core volume adjusting for power rating. This means designers have favored very high powers and high-power densities, irrespective of the size, even though the reactor will probably melt itself when conditions deviate from the carefully defined accident conditions. Below, we see how nuclear reactor power ratings have increased since inception, logistically approaching the size and complexity limits of practical turbomachinery and mega projects. Size and power are decoupled. Why seek the highest power? To reduce cost because it means the reactor materials are being maximally utilized per unit time. Nuclear reactor power ratings over time reproduced from 1. EPR (1660 MWe) and other reactors not shown.
The alternative is 100s of reactors producing the same total power as a few very large units. Nuclear utilities and operators often believe that reactor count is an important part of the operating cost and complexity. The count of micro reactors to achieve a power level is neither here nor there. It’s like trying to scare people by quoting the number of LiPo cells in a battery pack, or the number of transistors in a chip, or the number of car engines on the road. It is a very large number! For one, the reactors will probably all be coupled to one large BoP, achieving similar economies of scale on the power plant and turbine island side. Each reactor may require its own control system and could suffer from less efficient RPVs, HXs, and tubing – but the mere number of units may well have only a small effect on the total cost that is outweighed by economies of factory production. Similar production economies occur with large aircraft or automobiles which are produced at rates of ~2000 and ~100M per year, respectively.
The principal way reactors fail is when operators are unable to sustain reactor cooling. When a reactor is turned off, it still produces roughly 7% of its full power as decay heat falling off with a power law of roughly -0.2 over the course of hours and weeks. But if cooling cannot be sustained continuously for any reason, this decay heat can be sufficient to cause fuel failures and fission product release. To make sure this does not happen, the reactor needs to run at sufficiently low power ratings, so that even if the operators cannot provide cooling, the reactor can cool itself or can manage to remain at safe temperatures. I first discuss power density, and surface area to power ratio (SAPR) metrics, and then consider a preliminary approach to define safety: limited power levels.
Power rating and size determine the power density of the reactor. Higher power densities are more difficult to passively cool down. Higher power densities also lead to Xenon poisoning of the reactor core, which can prevent the reactor, depending on the concept from changing power quickly. PWRs in development have too high a power density to quickly change power to match demand because of Xenon poisoning. To overcome Xenon poisoning, they use excessive control rods or other neutron control systems. For some reactors, it takes hours and sometimes days to be restarted once it has been shut down.
HTGR tend to have sufficiently low power rating for their size to limit the worst-case accident temperatures from exceeding fuel failure temperatures. In extreme cases like MMR, low power density also means it has negligible xenon poisoning and can change power very quickly without inordinate amounts of reactivity insertion potential, though temperature gradients in the ceramic components must be carefully accounted for.
MMR in particular has a lower decay heat power density than fusion systems like SPARC, DEMO, or ITER and orders of magnitude lower than other prototypical advanced reactors as shown in the figure below. A lower decay heat is more manageable by passive cooling systems, allowing the reactor to dissipate heat more easily and without damaging the reactor. The other aspect to consider is the maximum temperatures that can be safely maintained in the reactor. HTGR cores can withstand much higher temperatures than a fusion’s reactors metals, molten salts, and magnets. UNSC's 15 MWth MMR has a lower initial decay heat power density of 0.075 W/cm3, less than DEMO’s 0.083 W/cm3 in the blanket and divertor.2 The comparison would be less favorable for fusion 1 hour after shutdown when fusion’s decay heat is almost equal to fission’s decay heat.
Low enough power density also eliminates the need for water pool storage of used nuclear fuel. Current reactors produce used nuclear fuel that must be stored in large 12 m deep water pools for 2-5 years before being put into dry-storage casks. Reducing power density and decay heat can eliminate the wet storage and the fuel pool accident risk that was first experienced at Fukushima.
Another safety metric is the surface area to power ratio. SAPR is an indication of how much surface area the reactor has to dissipate excess heat during accidents. With sufficiently high SAPR, the reactor can dissipate all excess heat through conduction and radiation – totally passive and intrinsic heat transfer mechanisms that are basically guaranteed to work. Passive physical heat dissipation is based on physical laws and material properties and can occur through natural convection, conduction, or radiative heat transfer. The more intrinsic the heat dissipation mechanism, the stronger the argument for reduced safety systems. This makes radiative cooling and thermal conduction from an external surface superior to natural convection of liquid with internal flows. Natural convection can be mechanically obstructed and coolant pools can leak or become displaced, whereas conduction and radiation are intrinsic solid state physical mechanisms. In the context of IAEA’s passive system categories, 3 a Class A system requires no intelligent signals, no external power or force, has no moving parts, and has no working fluid. A Class B Safety system requires moving parts or fluids, but fundamentally relies on natural and passive mechanisms. An Active Safety system requires functional moving parts like pumps, may require operator action, and requires functional control systems.
If the power produced in the core is too high for the given surface area, the reactor temperatures can increase to the point where core components or structural components outside the core are damaged. Higher surface area to power ratio translates into a safer reactor as heat can be more easily dissipated by passive, solid state heat transfer. To summarize, there are a few knobs to improve resilience to decay heat: reduce power rating, increase surface area, or improve the thermal capabilities and temperature tolerance of the core materials. The last point can also include the use of a large heat sink in the reactor core, such as graphite blocks that can absorb heat and reduce temperature increases, as previously discussed.
Data for each technology architecture obtained from456and author’s analysis of industry reports and public information.
Li, “A Paradigm Shift Needed for Nuclear Reactors: From Economies of Unit Scale to Economies of Production Scale.” ↩
Someya et al., “Management Strategy for Radioactive Waste in the Fusion Demo Reactor.” ↩
IAEA, “Safety Related Terms for Advanced Nuclear Plants.” ↩
“IAEA Advanced Reactors Information System (ARIS) - Technical Data.” ↩
Sterbentz et al., “Special Purpose Nuclear Reactor (5 MW) for Reliable Power at Remote Sites Assessment Report.” ↩
“GE Hitachi Nuclear Energy BWRX-300 General Description. ” ↩
There are many ways to design a nuclear reactor to extract and utilize the nuclear heat. What are the principal design choices and trades for a nuclear system? Nuclear systems have many interacting subsystems and there are many choices and trades to consider with a multitude of effects on safety and cost, both subtle and drastic. And many of the choices are not straightforward to understand or predict.
For introductory purposes, we can distill the many technology choices to just a couple: fuel, coolant, temperature, size, and power rating as listed in the table below. Each usually has some partisan zealot, championing a particular choice and design path. As designers, we are forced to down-select technologies and we cannot forever be open to all the thousand combinations of reactor technologies. The diversity of design possibilities suggests many ways to the same end, but the fact is that one architecture can be best for a given set of goals.
There's a fun random reactor generator at (whatisnuclear.com)[https://whatisnuclear.com/random.html]
| Parameter | Options |
|---|---|
| Fuel Form | Oxide, carbide, nitride, metallic, molten salt, liquid metal. |
| Fuel Wrapper and Geometry | TRISO-matrix, metallic clad, ceramic clad, no clad, (geometry: cylinders, annuli, pebbles), fuel wrapped moderator |
| Fuel Type and Cycle / Enrichment | LEU converter, Natural U converter, HALEU converter, HEU burner, Pu burner, U-Pu breeder, Th-U breeder |
| Coolant and pressure | Helium, water, CO2, sodium, sodium heat pipe, molten salt (fluoride or chloride), other liquid metals, organic, other gases (H2, N2, air). Pressures of 1-15 MPa, typically 3-7 MPa for He |
| Moderator / Reflector | Graphite, water, heavy water, hydrides, Beryllium (no clad, ceramic, or metallic clad, composite / entrained) |
| Size | Physical dimension of the reactor [~1-6m diameter, 1-20m height] |
| Power Rating | Power rating per reactor core [0,inf] MWth |
| Temperatures | [150-1050 °C], 2000 °C+ for Nuclear Thermal Propulsion |
The average electrical powerplant in the US has a name plate capacity of 120 MWe and delivered capacity of 46 MWe when averaged over the year. These are not massive power plants!
The average US process heat facility in petroleum, chemical, paper, and food industries has a heat demand of 77 MWth. The figures below show the distribution of electrical power plants according to their delivered power rating. Over half the power supplied comes from power plants less than 500 MWe. Lower power ratings are even greater contributors when we consider other energy generation devices like automobiles, ships, and aircraft. One should also consider transmission and distribution costs which can vary widely depending on the degree of centralization and the specific location, but generally can be on the order of half the delivered cost of power and in the range 1-15 cents per kWhe.
A single 1GWth reactor is unable to supply heat to 10 dispersed 100MWth users, but a 100MWth reactor can be replicated to serve a gigawatt user. From a business perspective, large reactors sacrifice the ability to serve a wide range of geographically distributed and smaller end-users.
It has been proposed that nuclear continue to try multi-gigawatt scale deployments in the form of nuclear hubs - megaproject facilities where massive power plants are collocated with large power users. This can often make sense if there is already an industrial zone, ready to receive a large central power plant. But the reality is that most power generation is at a much smaller scale and geographically distributed, by physical requirement of the end-user or the shear impracticality of centralized power projects.
We have existing infrastructure that has evolved over centuries with influence from waterways, roads, cities, and the resources at hand. We should consider matching new solutions to the existing infrastructure. Creating new gigawatt scale hubs could devolve into the usual predicament of the central planner: underutilized and unwanted infrastructure.
The risk related to nuclear fission is first described and it is argued that aversion to nuclear at the local level is not as unfounded as the nuclear community would make it out to be, considering the alternatives. It is shown that widescale democratic adoption can only be achieved through a different approach to risk reduction. Instead of reducing risk through reduced probabilities and militaristic operations, risk can be reduced by lowering consequences primarily through the use of passive safety mechanisms and inherently safe design characteristics that consider the hazards surrounding the fission products. This was the predominant approach to nuclear safety in the 1990s and gave rise to passive safe designs such as AP1000. In the 1990s both government and public support were low for nuclear energy. Since only the Vogtle units have come online in the last 30 years, it is still not clear, if such a strategy will be ever commercially viable. Nevertheless, this is the direction for nuclear design behind this thesis and many recent SMR and micro reactor demonstration and commercialization efforts, that push passive and inherent safety to the extreme, considering designs where risk can be evaluated deterministically.
Nuclear reactors produce radioactive fission products, roughly a third of the periodic table, and these radioactive isotopes pose a notable financial and health risk during accidents where various hazards can help unleash the fission products outside the fuel clad. A nuclear reactor must address this source term head on. It must protect the powerplant investment and surrounding community from the radioactivity. To do so, it must contain fission products and radiation by remaining at safe temperatures across the condition space including operations, beyond design basis accidents (BDBA), and disposal.
We must not conflate the existence of the fission products with potential consequence. A source term can only have a large consequence if there is a driving force to energize and disperse the fission products. In a nuclear reactor, that energetic driving force is usually the decay heat power, rapid power increases during a reactivity accident, unexpected loss of cooling, or a chemical energy release – but can be any of the hazards shown in Table 4. Removing the driving forces and hazards removes the consequence. This is as far as one can go to reduce consequence while still generating neutrons and fission products. All fission reactors have a source term, but not all reactors have an energetic driving force to turn those fission products into a consequence. A nuclear corolla should aim to reduce energetic driving force and contributing hazards that can create a consequence from fission products. Achieving this in a cost-effective manner, has remained elusive.
Aversion to nuclear deployment is more subtle than just an overreaction or an overinflated risk perception. While deaths per TWh attributed to nuclear power, including those from black swan accidents, are on par with renewables,1 and while reactor accident event frequency has been reduced from 0.01 in the 1970s to 0.003 events per plant per year worldwide through industry reform and learning, we have simultaneously seen the less frequent but extremely high-cost accidents every ~6,000 reactor-years. There have been 24,000 commercial reactor years and 4 of the commercial ones have undergone meltdowns. These accidents pose a low probability but high consequence financial risk relative to alternative technologies.2
The majority of operating nuclear power plants are statistically safe on death per TWh metrics because the death statistics are a shallow way of measuring consequences, and the statistics are theoretically diluted across very large populations. But the local adverse effects of an accident to the utility, asset owners, and customers are concentrated and crushing. Coal and fossil fuels are statistically less safe by the same metric, but any climate change and health effects are diluted worldwide in a real and practical way. The reality is that there are cost competitive alternatives to nuclear energy, and these systems are not able to fail catastrophically like a nuclear reactor because they do not have fission products onsite. Why expose oneself to the even small probabilities of extreme consequences when there are alternatives?
Ordinarily, comparisons are made on the deaths per energy unit delivered, as in the below figure. But the public is more concerned with significant hardship than with simple deaths. A better metric than death rates is a death equivalent consequence like displacement or financial loss. It appears likely that excess death rates from accidents like TMI and Fukushima are too low or too difficult to measure over the decades. But the financial cost of a nuclear cleanup and forced population displacements of the region surrounding the power plant can be considered equivalent to deaths. Forced displacement, prolonged financial hardship, loss of land are equivalent to death. Financial losses diluted over large populations can be converted to deaths even without a single actual death.
Accident events and damage reproduced from3; death rates per unit energy delivered from4.
The below equation represents the concept of risk as the probability of an event multiplied by its consequence. 5 added a power of to the consequence to incorporate the idea that perception of consequence does not always match the real consequence. While we can assume perception matches reality, we suspect that the public is an adherent to Murphy’s Law, and increases to compensate lower theoretical probabilities from engineers, a kind of hedge against the word of those who stand to benefit most and often have no skin in the game. With , risk is often perceived simply as the potential consequence.
We have seen nuclear accidents play out over the last 60 years, with a reported probability of about 1/100 reactor failures with severe local consequences, perhaps double if including close calls, and extra dangers associated with spent fuel pools. This comes out to about 1/6,000 probability of a severe nuclear accident per reactor year. The consequences of these accidents have proven substantially different from other sources of energy. In particular, the health consequences have been limited or comparable to other sources of energy, while the financial consequences have been immediate and long lasting, staggeringly high and concentrated to the regions around the reactor.
Direct effects of nuclear accidents have historically been geographically constrained to within tens of kilometers and at most a hundred kilometers if the weather is particularly unfavorable. There is little reason to believe nuclear accidents can directly have global effects because radioactivity is massively diluted with distance and travel time, and weather is a comparatively slow phenomenon relative to the most relevant radioisotopes. For nuclear, the risk of serious financial or health disaster is a local matter with local consequence.
Fossil fuels damage at both local and global scales. The pollution around fossil fuel plants reliably increases respiratory diseases and cancers. The production of greenhouse gases is a global effect, but its financial and health impact have not yet managed to justify a full decarbonization at the expense of slower economic development. Financial losses due to changes in climate, should the predictions ever materialize, may be recouped through newly available and useful land at higher latitudes. For fossils, in the worst case of power plant destruction, the utility or insurer will lose the value of the power plant and a new one can be built. There are no century-long cleanup efforts for fossil power plant accidents. There are no bankruptcies at the city, company, or country level. But the group risk is higher because of the health consequences of polluting the atmosphere and perhaps some climate change effects could materialize at some point.
Financial consequences of fossil fuel use are not clearly measurable owing to the great dilution, long time frames, and guesswork involved in its estimation. Fossil fuel health consequences are globally diluted. The probability of death-like consequences from fossil fuel pollutants is in the USA, 6 equally applied to the entire population.
From a global planner perspective, nuclear makes sense if the nuclear risk is less than the fossil risk. The risk is computed for each course of action below. The risk of each choice is the product of the population exposed, the probability of consequence, and the consequence itself which is a death or death equivalent consequence. For nuclear the reactor accident probability multiplied by the local population is considered. For fossils, the probability of death from emissions multiplied by the total population is considered.
We can drop the , the consequence, since it's on both sides. Compared to fossils, nuclear doesn't have to have as low an event probability because its accidents can be locally confined. That is . The risk averse global planner chooses nuclear if the following inequality is met.
But for the local planner and local population, where nuclear only makes sense if the nuclear event probability is lower than the fossil event probability.
The problem is that and are perceived as roughly equivalent and could well be about the same in reality. Historically, we know that most of existing reactors fail at a rate of about 1/6000 per year, with extreme costs, concentrated on the local populations and countries of operation. With this history and this comparison, a rational, local population sees roughly equivalent risk from either choice. But more likely, the local population perceives , in deference to Murphy’s Law. Fossil exposures are mostly conventional deaths and not easily traceable to fossils – it's difficult to blame fossil fuels for the premature cancer and respiratory deaths of a 60-80 year old, especially considering that fossil burning has been the norm for three centuries. And one can blame the whole fossil fuel industry, not any single fossil fuel emitter. Nuclear accident consequences have a clear source. It’s easy to connect the financial and death equivalent consequences related to a specific nuclear reactor accident.
The local population also has no influence over the fossil fuel emitters. Their exposure to fossil risks is not affected by their local choice of nuclear or fossil energy. For the local population, choosing nuclear only adds to the fossil risk. On the other hand, the global planner is willing to put some populations at elevated risk to achieve lower overall risk. While globalist autocratic societies are on the rise, we hope self-determination by local people remains the way of the west. With this understanding, massive nuclear deployments in democratically run countries requires a new approach to risk reduction – one based on a deterministic approach that better approximates the public’s respect for Murphy’s Law.
The typical design approach for nuclear reactors has been to avoid accidents at all costs because the fuel can fail catastrophically in such events, due to melting or rupture. As a result, nuclear powerplants have become overengineered behemoths with a complex web of safety systems aimed at reducing the probability that accidents occur and trying to contain them when they do occur. Costs balloon rapidly, in large part due to paperwork but also due to quality control, material costs, and inefficient construction.7 Accidents are yet to happen in GENIII and III+ reactors but GENI and II designs’ accidents have resulted in unexpected fission product release and loss of public trust that continues to limit the industry’s growth in certain regions of the world. To become viable decarbonization tools, nuclear reactors must simultaneously eliminate black-swan risk and reduce costs.
Reducing reactor accident rates is expensive in large and traditional nuclear reactors. For new reactors and new components including passive safety systems, the probabilities are educated guesses that remain to be tested in time. During licensing, reactor designers make a safety case by using Probabilistic Risk Assessment (PRA). They analyze event trees that can lead to catastrophic accidents and assign probabilities to the events to come up with “core-damage frequencies.” PRA emerged as a tool to figure out where the engineering design should be focused to reduce risk most efficiently. Worst case high consequence accidents like complete Loss of Coolant Accidents (LOCA) are not likely and somewhat impossible to deal with, so the focus shifted towards dealing with lower consequence but higher probability accidents like partial LOCAs which would have more impact on the overall risk. This is a sensible way to lower the overall risk as economically as possible but still leaves reactors exposed to worst case black swan accidents that could occur despite very low theorized probabilities.8
But even very low probabilities lead to reasonably high chances of failure at very high deployments. This is why the operating reactors rely on containment for both predicted low probability events and unknown events, the containment limits the radioactive release and exposure of it to humans. Those failures, rare as they are, despite the ability of containment to reduce off-site dose consequences, still lead to a global slump in financial and political support – the nuclear resets. The black swan risk is always there. Regulators, bankers, and the public are ready to slow down nuclear adoption, throttle financing and approvals, and heap on a few more regulations. Does the public care about these estimated PRAs considering the history of nuclear accidents and prior erroneous claims? No matter how low the estimated probability or how much extra CAPEX and OPEX goes into lowering the probability, the public is likely to continue to respect Murphy’s Law and will pick amongst the many available alternatives.
Minimizing probabilities is a fool’s game that can only increase costs because the underlying problem is not solved. We should avoid building and operating reactors in such a way that they can melt during inconvenient conditions. The alternative approach to risk reduction is to lower consequences and embrace accidents through passive safety systems as almost all new reactors world-wide have limited to full reliance on passive safety. In CA-HTGR, the probabilities in PRA are generally set to 1 and the safety analysis becomes more deterministic. For CA-HTGR, consequences of accidents are negligible because of the inherent safety mechanisms that can deal with the decay heat. This means that reactor designs should not have to include elaborate systems to lower the theoretical probability of accidents from happening.
This deterministic, Murphy’s Law approach accepts that worst case accidents will happen at some point, commonly refer to as the maximum credible accident, and then designs the reactor and fuel so that the worst-case accident has low and if not zero nuclear related consequences. This is achieved by reducing the hazards and driving forces that can turn fission products into a consequence. More practically, this can be done by designing the reactor to passively remain at safe temperatures in worst case accident conditions including simultaneous Beyond Design Basis Accidents (BDBA). The ability to safely dissipate the reactor’s energy can be relegated to passive physical mechanisms rather than active systems.
No one doubts that a nuclear reactor can be designed this way. But the idea that it can be done at competitive costs remains in question. The reduction in consequence has far reaching implications beyond potential public acceptance. Using passive heat dissipation systems, the reactor can be simplified with fewer safety systems and parts. Rather than trying to avoid accidents through perfect operations and safety systems, these reactors would rely on physical material properties to withstand accidents rather than external or active systems. This means worst case accidents can happen without fission product release – a radical shift from today’s reactors in which mechanical cooling capability is required to avoid meltdown. Without conventional meltdown risk, these reactors may be treated like non-nuclear industrial sites with a corresponding reevaluation of costs and applications. The nuclear corolla takes this approach aiming for a cost profile of CCNG if the nuclear regulation treats it as such.
Ritchiem and Roser, “Modern Renewables and Nuclear Energy Are Not Only Safer but Also Cleaner than Fossil Fuels.” ↩
Wheatley, Sovacool, and Sornette, “Reassessing the Safety of Nuclear Power.” ↩
Wheatley, Sovacool, and Sornette. ↩
Ritchiem and Roser, “Modern Renewables and Nuclear Energy Are Not Only Safer but Also Cleaner than Fossil Fuels.” ↩
Weinberg, “Science and Trans-Science.” ↩
Ritchiem and Roser, “Modern Renewables and Nuclear Energy Are Not Only Safer but Also Cleaner than Fossil Fuels.” ↩
Eash-gates, Kavlak, and Mcnerney, “Sources of Cost Overrun in Nuclear Power Plant Construction Call for a New Approach to Reactor Engineering Design.” ↩
Zinkle et al., “Accident Tolerant Fuels for LWRs: A Perspective.” ↩
No - it's not "too cheap to meter." But it also shouldn't be prohibitively expensive to construct. Estimating nuclear energy costs compared to other energy generating assets is challenging and necessary to make financing decisions. We just have to be aware as to who has their fingers on the spreadsheet. Is it a wind and solar zealot, a fossil profiteer, or a nuclear startup? The following is a little exercise to see what the cost limits might be for nuclear energy.
Fusion is generally touted by many as an energy "Holy Grail." Indeed, it appears to have similar qualities, being both perpetually elusive and miraculous, able to solve all mankind's problems. Media reporting tends to discuss the benefits of fusion with misleading and false statements and no discussion of fusion’s negative attributes. The financial and practical perspective of fusion based power is missing.